Information-theoretic foundations of quantum mechanics

Quantum theory from binary questions: by assuming that information is acquired through elementary yes–no questions to nature, one is naturally led to the basic probabilistic and algebraic structure of quantum theory.

Motivated by Wheeler’s idea of "it from bit" — the view that information is the most fundamental constituent of physical reality — we formulated one of the first information-theoretic approaches to quantum theory. Its basic premise is that every quantum system carries only a finite amount of information. In particular, an elementary system may be said to carry one bit, represented by the truth value of an elementary proposition such as "the spin is up along the z-direction."

Within this framework, many characteristic features of quantum theory can be understood as consequences of limited information content. The finiteness of information implies that increased knowledge about one observable must be accompanied by decreased knowledge about complementary ones. Entanglement reflects the fact that, in composite systems, information can reside more in correlations than in the individual subsystems. The conservation of total information, in turn, is reflected in the unitary nature of quantum dynamics.

These considerations led naturally to an information-theoretic reconstruction of quantum theory.